The Lomax distribution also known as Pareto distribution of the second kind or Pearson Type VI distribution has been used in the analysis of income data, and business failure data. It may describe the lifetime of a decreasing failure rate component as a heavy tailed alternative to the exponential distribution. In this paper we consider the estimation of the parameter of Lomax distribution. Baye’s estimator is obtained by using Jeffery’s and extension of Jeffery’s prior by using squared error loss function, Al-Bayyati’s loss function and Precautionary loss function. Maximum likelihood estimation is also discussed. These methods are compared by using mean square error through simulation study with varying sample sizes. The study aims to find out a suitable estimator of the parameter of the distribution. Finally, we analyze one data set for illustration.
It comprises the study of Hydrogen Chemistry and their applications.
Apart from these, It contains The stoarge, transportation of hydrogen along with the preparation of hydrogen.
The influence of pinching on the growth, flowering pattern and yield of butte...Premier Publishers
A field experiment was conducted at Africa University farm, Mutare, Zimbabwe to evaluate the effects of pinching on the growth, flowering pattern and yield of butternuts (Cucurbita moschata). The experiment was laid as a Randomized Complete Block Design. Cucurbita moschata was used as the test crop with evaluation being the yield, flowering pattern, branches, stems and fruit weight. Treatment groups included no pinching, pinching at 2nd node, pinching at 4th node and pinching at 6th node. Treatments with pinching had the highest yield(18.80t/ha) and highest number of flowers(5.10) compared to plants with no pinching. Pinching plants at 6th node increased the number of branches compared to pinching plants at 2nd node. The number of stems were highest (3.65) in pinched plants (TRT 4) compared to plants which did not receive pinching. General trends showed that number of stems increased as pinching was done at a later stage. The number of fruits harvested in plants per treatment corresponded to the fruit weight gained. The greater the number of harvested fruits, the higher the corresponding weight and vice versa. These findings indicated that pinching plants at a later stage of its growth promotes the growth, flowering pattern and yield of plants.
Experimental investigation of four stroke single cylinder rope brake dynamome...Premier Publishers
The present work is focused on the effects of waste cooking oil based methyl ester and its blends with petrodiesel on a single cylinder, 4 stroke, naturally aspirated, direct injection, water cooled, rope brake dynamometer assisted CI engine at varying loads. The physical and chemical properties of WCO based methyl ester were determined using standard ASTM methods. The suitability of WCO based methyl ester and its blends were evaluated through determining the performance and emission characteristics of CI engine. These results were compared to petrodiesel for validation. By analyzing these results, it was observed that the performance and emission characteristics were shown both satisfactory and unsatisfactory results. This was due to lower calorific value and high viscosity of waste cooking oil methyl ester resulted delay in combustion. From the critical analysis, it was observed that B20 of WCO based methyl ester reserved 32.2% brake thermal efficiency slightly greater than petrodiesel i.e. 32% without any engine modifications. It is concluded that B20 of WCO based methyl ester is suitable with no modification in engine.
Knowledge, adoption and constraint analysis of chilli technology in Char area...Premier Publishers
In the present study, Knowledge Index (KI) and Adoption Index (AI) were developed to measure the knowledge level and Adoption level of Chilli Technology of farmers in Char Area of Bangladesh. A preliminary test of thirty knowledge items related to chilli cultivation technology was administered to 38 chilli farmers who were involved in chilli production in island char areas. Data were collected during February to March 2008 through interview schedule. The Knowledge Index (KI) ranged from 71 to 99 and Adoption Index (AI) ranged from 68 to 98. A correlation coefficient of KI and AI was 0.97 which indicated that a high relation exists between Knowledge Index (KI) and Adoption Index (AI). The major constraints are ignorance about improved seeds and cultivation practices, chemicals with doses and method of application, scientific method of storage, etc. The major economic and physical constraints are the high cost of the seed of improved cultivars, non-availability of funds, etc. It was recommended that the farmers be guided through extension visits to teach them adoption of new technologies related to Chilli production. The study will help researcher, agricultural extension worker, policy maker and NGOs to address and analyse the issues related to knowledge, adoption and constraints of not only chilli production but also other field and horticultural crops production.
It comprises the study of Hydrogen Chemistry and their applications.
Apart from these, It contains The stoarge, transportation of hydrogen along with the preparation of hydrogen.
The influence of pinching on the growth, flowering pattern and yield of butte...Premier Publishers
A field experiment was conducted at Africa University farm, Mutare, Zimbabwe to evaluate the effects of pinching on the growth, flowering pattern and yield of butternuts (Cucurbita moschata). The experiment was laid as a Randomized Complete Block Design. Cucurbita moschata was used as the test crop with evaluation being the yield, flowering pattern, branches, stems and fruit weight. Treatment groups included no pinching, pinching at 2nd node, pinching at 4th node and pinching at 6th node. Treatments with pinching had the highest yield(18.80t/ha) and highest number of flowers(5.10) compared to plants with no pinching. Pinching plants at 6th node increased the number of branches compared to pinching plants at 2nd node. The number of stems were highest (3.65) in pinched plants (TRT 4) compared to plants which did not receive pinching. General trends showed that number of stems increased as pinching was done at a later stage. The number of fruits harvested in plants per treatment corresponded to the fruit weight gained. The greater the number of harvested fruits, the higher the corresponding weight and vice versa. These findings indicated that pinching plants at a later stage of its growth promotes the growth, flowering pattern and yield of plants.
Experimental investigation of four stroke single cylinder rope brake dynamome...Premier Publishers
The present work is focused on the effects of waste cooking oil based methyl ester and its blends with petrodiesel on a single cylinder, 4 stroke, naturally aspirated, direct injection, water cooled, rope brake dynamometer assisted CI engine at varying loads. The physical and chemical properties of WCO based methyl ester were determined using standard ASTM methods. The suitability of WCO based methyl ester and its blends were evaluated through determining the performance and emission characteristics of CI engine. These results were compared to petrodiesel for validation. By analyzing these results, it was observed that the performance and emission characteristics were shown both satisfactory and unsatisfactory results. This was due to lower calorific value and high viscosity of waste cooking oil methyl ester resulted delay in combustion. From the critical analysis, it was observed that B20 of WCO based methyl ester reserved 32.2% brake thermal efficiency slightly greater than petrodiesel i.e. 32% without any engine modifications. It is concluded that B20 of WCO based methyl ester is suitable with no modification in engine.
Knowledge, adoption and constraint analysis of chilli technology in Char area...Premier Publishers
In the present study, Knowledge Index (KI) and Adoption Index (AI) were developed to measure the knowledge level and Adoption level of Chilli Technology of farmers in Char Area of Bangladesh. A preliminary test of thirty knowledge items related to chilli cultivation technology was administered to 38 chilli farmers who were involved in chilli production in island char areas. Data were collected during February to March 2008 through interview schedule. The Knowledge Index (KI) ranged from 71 to 99 and Adoption Index (AI) ranged from 68 to 98. A correlation coefficient of KI and AI was 0.97 which indicated that a high relation exists between Knowledge Index (KI) and Adoption Index (AI). The major constraints are ignorance about improved seeds and cultivation practices, chemicals with doses and method of application, scientific method of storage, etc. The major economic and physical constraints are the high cost of the seed of improved cultivars, non-availability of funds, etc. It was recommended that the farmers be guided through extension visits to teach them adoption of new technologies related to Chilli production. The study will help researcher, agricultural extension worker, policy maker and NGOs to address and analyse the issues related to knowledge, adoption and constraints of not only chilli production but also other field and horticultural crops production.
Sharing gains of the potato in Kenya: A case of thin governanceSharing gains ...Premier Publishers
The potato offers a good alternative for diversification from maize, the staple food in Kenya. This article presents the results of a study on the potato marketing system, the factors affecting prices and the predominant governance system impacting on the market. Survey data were collected from 402 farmers in the three potato growing regions and addition information on monthly prices in major markets was provided the Ministry of Agriculture. There were also semi-structured interviews with the major actors in the potato sector.
Potato marketing exhibits the captive governance structure with traders collaboratively acting as the lead firm. An analysis of the split in selling price between the various players indicates that margins were concentrated at the coordination of marketing activities as opposed to the production activities. Coordination activities took about 40% of the consumer price. Besides the market channel used, the production region, the size of the land cultivated and the yields obtained determined the price obtained by the farmers. Given the distribution of the value added in the chain and the current dominance of traders, we argue in favour of upgrading the value chain and giving more power to the farmers and their organizations.
Current status of commercial solid waste generation, composition and manageme...Premier Publishers
This study determined the quantity, composition, the levels of remaining recyclable materials, and to evaluate treatment methods for commercial solid waste (CSW) in Phnom Penh, Cambodia. Waste samples were collected from 52 commercial sectors including hotels, restaurants, internet cafés, guesthouses, beer gardens, markets, schools, microfinance agencies and shops. The waste was collected daily for two weeks in 2013 and separated into 23 categories. The main composition of CSW were food (50-60%), followed by plastic and paper (30-40%) and glass (5-6%). The waste generation in kg/table/day was 4.83 (large restaurants), 3.36 (medium restaurants), 2.23 (beer gardens), 1.94 (internet cafés); in kg/room/day was 0.69 (3-star hotels), 0.45 (large guesthouses), 0.37 (medium and small guesthouses), 0.097 (small hotels) and in kg/person/day was 0.153 (family marts), 0.15 (ministries), 0.12 (council of ministers), 0.12 (supermarkets), less than 0.10 (shops and schools). Sorted waste was food, followed by glass bottles, paper, PET bottles, aluminium cans and steel. The remaining recyclable materials were food, plastic, paper, steel and aluminium cans. Well sorting activity was conducted by internet cafés and restaurants, followed by family marts, schools, beer gardens and guesthouses. If food waste and other recyclable materials were completely sorted, 61% of current waste could be minimized.
Theme of love and mysticism in English and Pakistani poetry with reference to...Premier Publishers
The original concept of love may differ from person to person as well as society to society and culture to culture. It can be interpreted differently. Love is a remarkable thing which has bounded the society and the people always to each other. Mysticism would best be assumption of as a gathering of individual practices, sermons, scripts, institutes, societies, and familiarities aimed at human alteration, variously defined in different traditions. The person is known as William James which has tried to clear the concept of mysticism. The research will find out how the works of two different poets living in different continents and having opposite cultural backgrounds are addressing the same ideas and incorporating similar notions about mysticism and love. This study is devised out of curiosity weather William Wordsworth and Ameer Hamza Shinwari’s poetry contains the elements of mysticism and love. This study tries to see the different dimension of his work and give the proper and the required conclusion.
The latest innovation from Koodos following on from its successful Koodos for Teens course comes Koodos International. A fun and interactive course lead by experienced staff to assist with either permanent or temporary overseas integrating into NZ life and culture.
Evaluation mutagenic potential of pesticides through bioassays with Allium cepaPremier Publishers
The evaluation mutagenic potential of pesticides most used in southeastern Brazil, through bioassays with Allium cepa, it was an important study to understand harmful action of two classes of pesticides widely used in Brazil. The effects significant of cytotoxic and genotoxic in Allium cepa were evaluated in the following concentrations: 10 μL/mL, 25 μL/mL and 50 μL/mL, for Pyraclostrobin and Iminoctadine being in all cases compared to the negative and positive controls. With the results obtained it was possible to verify that the two pesticides have the ability to promote genetic changes. This study is a consequence of numerous complaints about harmful effects these substance, since small changes in DNA can cause irreversible problems the human health.
Growth and yield of tomato, Napier grass and sugarcane crops as influenced by...Premier Publishers
The effect of wastewater irrigation on plant growth and yield of tomato, Napier grass and sugarcane crops was compared with that of ground water irrigation. Treatments included untreated wastewater (UWW) treated wastewater (TWW) and ground water (GW) as control. The results obtained, plant height, number of fruits/plant, dry biomass g/plant and number of branches/plant of tomato (78.46 cm, 45.88, 15.49 and 11.41) and (75.13 cm, 41.48, 14.42 and 10.28) were significantly higher in the UWW and TWW compared to GW. The UWW and TWW irrigated Napier grass gave the highest growth and yield, compared to that of GW irrigation. Plant height, number of leaves/plant, leaf length, leaf width and number of tiller were 188.46 cm, 83.62, 93.62 cm, 2.52 and 13.2 in UWW and 182.68 cm, 69.75, 88.67cm, 2.29 and 10.39 in TWW and these are significantly higher as compared to that of GW irrigation. Wastewater irrigation of sugarcane increased cane length, number of nodes/cane, number of leaves, cane diameter and cane weight significantly as compared to control GW are 191.86 cm, 22.48, 39.3 and 2.30 cm in UWW and 149.4 cm, 20.54, 27.53 and 2.22 cm in TWW and compared to that of GW irrigation.
Role of Banks on Agricultural Development in BangladeshPremier Publishers
The aim of this study is to determine the role of banks on agricultural development. Agricultural development is determined in respect of crops, purchase and installation of irrigation equipment, livestock, marketing of agricultural goods, fisheries, poverty alleviation and income generating activities. A total number of 50 respondents were interviewed through semi-structure interview schedule for obtaining primary data. Secondary data was collected from annual reports of Bangladesh Bank during period from 2010 to 2014. The disbursement of agricultural credit on crop production is increased up to Tk. 71.31 billion in 2014 from Tk.33.19 billion in 2010. Subsequently, the disbursement of agricultural credit on purchase and installation of irrigation equipment, crop production, marketing of agricultural goods, fisheries are changed significantly with time. The credit on poverty alleviation increased up to Tk. 18.64 billion in 2014 from Tk.13.61 billion in 2010. The result indicates that bank plays on a significant role on agricultural development in Bangladesh. Timely flow of agricultural credit can meet farmers demand to ensure agricultural productivity. The study will help governmental policy makers and NGOs to address and analyze the issues of agricultural sector to provide loan to the farmers for promoting actual development in this sector.
Bouguer anomaly and free-air anomaly correlation signatures in parts of Benue...Premier Publishers
Topographic values in the study area range from 80m to 170m. The rock type comprises Basement Complex at the west bounded by River Niger, and sedimentary rock type in the east. Density measurements of various rocks were taken with the highest bulk density from the metamorphic schist (2.77gm/cm3), followed by igneous rock olivine gabbro (2.73gm/cm3), and sandstone (2.35gm/cm3). Results of gravity survey revealed a mean Bouguer anomaly of +12.15 mgals and a mean free air anomaly of +22.0 mgals. Interpretation of gravity measurements revealed the existence of a fracture at Gboloko NE-SW axis, a synclinal fold axis at about 5.5km west of Gboloko (between the Staurolite Schist and Cordierite-Tourmaline schist). The Basement-Sedimentary boundary is characterized by a drop in residual Bouguer anomaly from positive to negative at about 6km east of Gboloko. The thickness of the sediments is about 0.90km at the northern part of the Basement-Sedimentary boundary, and about 2.0km in the south, thus suggesting a progressive increase in sedimentary thickness at the western edge of the Benue trough. The Free-air anomaly ‘highs’ correspond to Bouguer anomaly ‘highs’ and tied to areas of high topography and bands of weathered, lateritized sediments. The Bouguer anomaly profiles exhibited reliable signature changes at the rock boundaries, thus a supportive tool for delineation of those border areas.
Counterfeit Herbal Medicine adulterated with chemical drugs in Indonesia: NAD...Premier Publishers
Herbal medicine is widely used in Indonesia. Thus, counterfeit herbal medicines are a great concern given the negative impact to individual and population health. This paper used data drawn from the National Agency of Drug and Food Control (NADFC/BPOM)of Indonesia to describe the counterfeit trend against registered herbal drugs from 2011 to 2014, and further analyses were performed to discover the types of the fraud, the impact to the health and conventional drugs that could be used as substitutes for herbal drugs. The research found that the amount of falsified medicines is increasing along with the increasing number of registered herbal drugs. From the data obtained, similar falsified herbal drugs were identified for both life style drugs (51%) and health-related condition drugs (49%). In addition, almost all falsified herbal drugs are adulterations plus tampering (81%). The most significant substitute chemical drug is paracetamol.
Characteristics of coronary artery ectasia and its association with carotid i...Premier Publishers
This study was conducted to uncover the relation between coronary artery ectasia (CAE) and markers of atherosclerosis. A total of 1611 coronary angiograms were prospectively examined to find out patients with CAE. Those patients were divided into 2 groups: Mixed CAE with stenotic coronary artery disease (CAD) “group 1” and pure CAE “group 2”. Two control groups of age-adjusted subjects were selected consecutively in a 1:1 fashion; one with normal coronaries “group 3” (Pure CAE: normal coronaries) and the other with obstructive CAD only “group 4” (Mixed CAE: obstructive CAD). All recruited subjects underwent carotid intima-media thickness (IMT) and high sensitivity C-reactive protein (hs-CRP) level measurements. Out of examined angiograms, 35 subjects showed mixed CAE “group 1” and 26 showed pure CAE “group 2”. Age and gender-adjusted logistic regression analysis model revealed that significant independent predictors for CAE were: hypertension, smoking, absence of DM and hs-CRP level > 3 mg/L. Mean carotid IMT was significantly higher in group 2 than group 3 and in group 4 than group 1 (1±0.1 versus 0.4±0.2 mm and 1.4±0.4 versus 1±0.2 mm respectively, P < 0.001 for both). Mean hs-CRP level was significantly higher in group 1 than group 4 and in group 2 than group 3 (7±2 versus 3±0.8 mg/L and 6±2 versus 1±0.6 mg/L respectively, P < 0.001 for both). We concluded that atherosclerosis may not be the only plausible explanation for CAE.
Abstract:
A combination of exponential and Lindley failure rate model is considered and named it as exponential-Lindley
additive failure rate model. In this paper, we studied the distributional properties, central and non-central moments,
estimation of parameters, testing of hypothesis and the power of likelihood ratio criterion about the proposed model.
Key words: Exponential distribution, Lindley distribution, ML estimation, Likelihood ratio type criterion.
Predicting an Applicant Status Using Principal Component, Discriminant and Lo...inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Sharing gains of the potato in Kenya: A case of thin governanceSharing gains ...Premier Publishers
The potato offers a good alternative for diversification from maize, the staple food in Kenya. This article presents the results of a study on the potato marketing system, the factors affecting prices and the predominant governance system impacting on the market. Survey data were collected from 402 farmers in the three potato growing regions and addition information on monthly prices in major markets was provided the Ministry of Agriculture. There were also semi-structured interviews with the major actors in the potato sector.
Potato marketing exhibits the captive governance structure with traders collaboratively acting as the lead firm. An analysis of the split in selling price between the various players indicates that margins were concentrated at the coordination of marketing activities as opposed to the production activities. Coordination activities took about 40% of the consumer price. Besides the market channel used, the production region, the size of the land cultivated and the yields obtained determined the price obtained by the farmers. Given the distribution of the value added in the chain and the current dominance of traders, we argue in favour of upgrading the value chain and giving more power to the farmers and their organizations.
Current status of commercial solid waste generation, composition and manageme...Premier Publishers
This study determined the quantity, composition, the levels of remaining recyclable materials, and to evaluate treatment methods for commercial solid waste (CSW) in Phnom Penh, Cambodia. Waste samples were collected from 52 commercial sectors including hotels, restaurants, internet cafés, guesthouses, beer gardens, markets, schools, microfinance agencies and shops. The waste was collected daily for two weeks in 2013 and separated into 23 categories. The main composition of CSW were food (50-60%), followed by plastic and paper (30-40%) and glass (5-6%). The waste generation in kg/table/day was 4.83 (large restaurants), 3.36 (medium restaurants), 2.23 (beer gardens), 1.94 (internet cafés); in kg/room/day was 0.69 (3-star hotels), 0.45 (large guesthouses), 0.37 (medium and small guesthouses), 0.097 (small hotels) and in kg/person/day was 0.153 (family marts), 0.15 (ministries), 0.12 (council of ministers), 0.12 (supermarkets), less than 0.10 (shops and schools). Sorted waste was food, followed by glass bottles, paper, PET bottles, aluminium cans and steel. The remaining recyclable materials were food, plastic, paper, steel and aluminium cans. Well sorting activity was conducted by internet cafés and restaurants, followed by family marts, schools, beer gardens and guesthouses. If food waste and other recyclable materials were completely sorted, 61% of current waste could be minimized.
Theme of love and mysticism in English and Pakistani poetry with reference to...Premier Publishers
The original concept of love may differ from person to person as well as society to society and culture to culture. It can be interpreted differently. Love is a remarkable thing which has bounded the society and the people always to each other. Mysticism would best be assumption of as a gathering of individual practices, sermons, scripts, institutes, societies, and familiarities aimed at human alteration, variously defined in different traditions. The person is known as William James which has tried to clear the concept of mysticism. The research will find out how the works of two different poets living in different continents and having opposite cultural backgrounds are addressing the same ideas and incorporating similar notions about mysticism and love. This study is devised out of curiosity weather William Wordsworth and Ameer Hamza Shinwari’s poetry contains the elements of mysticism and love. This study tries to see the different dimension of his work and give the proper and the required conclusion.
The latest innovation from Koodos following on from its successful Koodos for Teens course comes Koodos International. A fun and interactive course lead by experienced staff to assist with either permanent or temporary overseas integrating into NZ life and culture.
Evaluation mutagenic potential of pesticides through bioassays with Allium cepaPremier Publishers
The evaluation mutagenic potential of pesticides most used in southeastern Brazil, through bioassays with Allium cepa, it was an important study to understand harmful action of two classes of pesticides widely used in Brazil. The effects significant of cytotoxic and genotoxic in Allium cepa were evaluated in the following concentrations: 10 μL/mL, 25 μL/mL and 50 μL/mL, for Pyraclostrobin and Iminoctadine being in all cases compared to the negative and positive controls. With the results obtained it was possible to verify that the two pesticides have the ability to promote genetic changes. This study is a consequence of numerous complaints about harmful effects these substance, since small changes in DNA can cause irreversible problems the human health.
Growth and yield of tomato, Napier grass and sugarcane crops as influenced by...Premier Publishers
The effect of wastewater irrigation on plant growth and yield of tomato, Napier grass and sugarcane crops was compared with that of ground water irrigation. Treatments included untreated wastewater (UWW) treated wastewater (TWW) and ground water (GW) as control. The results obtained, plant height, number of fruits/plant, dry biomass g/plant and number of branches/plant of tomato (78.46 cm, 45.88, 15.49 and 11.41) and (75.13 cm, 41.48, 14.42 and 10.28) were significantly higher in the UWW and TWW compared to GW. The UWW and TWW irrigated Napier grass gave the highest growth and yield, compared to that of GW irrigation. Plant height, number of leaves/plant, leaf length, leaf width and number of tiller were 188.46 cm, 83.62, 93.62 cm, 2.52 and 13.2 in UWW and 182.68 cm, 69.75, 88.67cm, 2.29 and 10.39 in TWW and these are significantly higher as compared to that of GW irrigation. Wastewater irrigation of sugarcane increased cane length, number of nodes/cane, number of leaves, cane diameter and cane weight significantly as compared to control GW are 191.86 cm, 22.48, 39.3 and 2.30 cm in UWW and 149.4 cm, 20.54, 27.53 and 2.22 cm in TWW and compared to that of GW irrigation.
Role of Banks on Agricultural Development in BangladeshPremier Publishers
The aim of this study is to determine the role of banks on agricultural development. Agricultural development is determined in respect of crops, purchase and installation of irrigation equipment, livestock, marketing of agricultural goods, fisheries, poverty alleviation and income generating activities. A total number of 50 respondents were interviewed through semi-structure interview schedule for obtaining primary data. Secondary data was collected from annual reports of Bangladesh Bank during period from 2010 to 2014. The disbursement of agricultural credit on crop production is increased up to Tk. 71.31 billion in 2014 from Tk.33.19 billion in 2010. Subsequently, the disbursement of agricultural credit on purchase and installation of irrigation equipment, crop production, marketing of agricultural goods, fisheries are changed significantly with time. The credit on poverty alleviation increased up to Tk. 18.64 billion in 2014 from Tk.13.61 billion in 2010. The result indicates that bank plays on a significant role on agricultural development in Bangladesh. Timely flow of agricultural credit can meet farmers demand to ensure agricultural productivity. The study will help governmental policy makers and NGOs to address and analyze the issues of agricultural sector to provide loan to the farmers for promoting actual development in this sector.
Bouguer anomaly and free-air anomaly correlation signatures in parts of Benue...Premier Publishers
Topographic values in the study area range from 80m to 170m. The rock type comprises Basement Complex at the west bounded by River Niger, and sedimentary rock type in the east. Density measurements of various rocks were taken with the highest bulk density from the metamorphic schist (2.77gm/cm3), followed by igneous rock olivine gabbro (2.73gm/cm3), and sandstone (2.35gm/cm3). Results of gravity survey revealed a mean Bouguer anomaly of +12.15 mgals and a mean free air anomaly of +22.0 mgals. Interpretation of gravity measurements revealed the existence of a fracture at Gboloko NE-SW axis, a synclinal fold axis at about 5.5km west of Gboloko (between the Staurolite Schist and Cordierite-Tourmaline schist). The Basement-Sedimentary boundary is characterized by a drop in residual Bouguer anomaly from positive to negative at about 6km east of Gboloko. The thickness of the sediments is about 0.90km at the northern part of the Basement-Sedimentary boundary, and about 2.0km in the south, thus suggesting a progressive increase in sedimentary thickness at the western edge of the Benue trough. The Free-air anomaly ‘highs’ correspond to Bouguer anomaly ‘highs’ and tied to areas of high topography and bands of weathered, lateritized sediments. The Bouguer anomaly profiles exhibited reliable signature changes at the rock boundaries, thus a supportive tool for delineation of those border areas.
Counterfeit Herbal Medicine adulterated with chemical drugs in Indonesia: NAD...Premier Publishers
Herbal medicine is widely used in Indonesia. Thus, counterfeit herbal medicines are a great concern given the negative impact to individual and population health. This paper used data drawn from the National Agency of Drug and Food Control (NADFC/BPOM)of Indonesia to describe the counterfeit trend against registered herbal drugs from 2011 to 2014, and further analyses were performed to discover the types of the fraud, the impact to the health and conventional drugs that could be used as substitutes for herbal drugs. The research found that the amount of falsified medicines is increasing along with the increasing number of registered herbal drugs. From the data obtained, similar falsified herbal drugs were identified for both life style drugs (51%) and health-related condition drugs (49%). In addition, almost all falsified herbal drugs are adulterations plus tampering (81%). The most significant substitute chemical drug is paracetamol.
Characteristics of coronary artery ectasia and its association with carotid i...Premier Publishers
This study was conducted to uncover the relation between coronary artery ectasia (CAE) and markers of atherosclerosis. A total of 1611 coronary angiograms were prospectively examined to find out patients with CAE. Those patients were divided into 2 groups: Mixed CAE with stenotic coronary artery disease (CAD) “group 1” and pure CAE “group 2”. Two control groups of age-adjusted subjects were selected consecutively in a 1:1 fashion; one with normal coronaries “group 3” (Pure CAE: normal coronaries) and the other with obstructive CAD only “group 4” (Mixed CAE: obstructive CAD). All recruited subjects underwent carotid intima-media thickness (IMT) and high sensitivity C-reactive protein (hs-CRP) level measurements. Out of examined angiograms, 35 subjects showed mixed CAE “group 1” and 26 showed pure CAE “group 2”. Age and gender-adjusted logistic regression analysis model revealed that significant independent predictors for CAE were: hypertension, smoking, absence of DM and hs-CRP level > 3 mg/L. Mean carotid IMT was significantly higher in group 2 than group 3 and in group 4 than group 1 (1±0.1 versus 0.4±0.2 mm and 1.4±0.4 versus 1±0.2 mm respectively, P < 0.001 for both). Mean hs-CRP level was significantly higher in group 1 than group 4 and in group 2 than group 3 (7±2 versus 3±0.8 mg/L and 6±2 versus 1±0.6 mg/L respectively, P < 0.001 for both). We concluded that atherosclerosis may not be the only plausible explanation for CAE.
Abstract:
A combination of exponential and Lindley failure rate model is considered and named it as exponential-Lindley
additive failure rate model. In this paper, we studied the distributional properties, central and non-central moments,
estimation of parameters, testing of hypothesis and the power of likelihood ratio criterion about the proposed model.
Key words: Exponential distribution, Lindley distribution, ML estimation, Likelihood ratio type criterion.
Predicting an Applicant Status Using Principal Component, Discriminant and Lo...inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The Odd Generalized Exponential Log Logistic Distributioninventionjournals
We propose a new lifetime model, called the odd generalized exponential log logistic distribution (OGELLD).We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The maximum likelihood method is used for estimating the model parameters and the Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real lifetime data.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
COMPARING THE CUCKOO ALGORITHM WITH OTHER ALGORITHMS FOR ESTIMATING TWO GLSD ...csandit
This study introduces and compares different methods for estimating the two parameters of
generalized logarithmic series distribution. These methods are the cuckoo search optimization,
maximum likelihood estimation, and method of moments algorithms. All the required
derivations and basic steps of each algorithm are explained. The applications for these
algorithms are implemented through simulations using different sample sizes (n = 15, 25, 50,
100). Results are compared using the statistical measure mean square error.
This presentation talks about some of the outstanding methods for Interpreting the complex machine learning black box models. One of the ideas is to use interpretable simple models to explain predictions using sophisticated black box machine learning models.
Model Agnostic methods are proven to have some specific advantages over the Model Specific Methods of Interpretability. This work demonstrates some of such results.
Evaluation of Agro-morphological Performances of Hybrid Varieties of Chili Pe...Premier Publishers
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2. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Ahmad et al. 055
)2(0,,0;1),;(
)1(
x
x
xf
where and are shape and scale parameters, respectively.
The survival function is given by
)3(1),;(
x
xR
and the hazard function is given by
)4(1),;(
)12(
x
xh
This paper is arranged as follows: Section 2, 3 and 4 discusses the Bayesian methodology using Jeffrey’s prior and
extension of Jeffrey’s prior information under different loss functions for estimation of the shape parameter of Lomax
distribution with known scale. Section 5, focuses in the simulation study and results to compare the estimators and
finally section 6 is the conclusion of the paper.
MATERIAL AND METHODS
Prior and Loss Functions
Recently Bayesian estimation approach has received great attention by most researchers. Bayesian analysis is an
important approach to statistics, which formally seeks use of prior information and Bayes Theorem provides the formal
basis for using this information. In this approach, parameters are treated as random variables and data is treated fixed.
An important pre-requisite in Bayesian estimation is the appropriate choice of prior(s) for the parameters. However,
Bayesian analysts have pointed out that there is no clear cut way from which one can conclude that one prior is better
than the other. Very often, priors are chosen according to ones subjective knowledge and beliefs. However, if one has
adequate information about the parameter(s) one should use informative prior(s); otherwise it is preferable to use non
informative prior(s). In this paper we consider the extended Jeffrey’s prior proposed by Al-Kutubi (2005) as:
RcIg
c
1,1
where
2
2
;log
xf
nEI is the Fisher’s information matrix. For the model (2),
1
2
c
n
kg
where k is a constant, with the above prior, we use three different loss functions for the model (2), first is the squared
error loss function which is symmetric, second is Albayyati,s loss function and third is the precautionary loss function
which is a simple asymmetric loss function.
It is well known that choice of loss function is an integral part of Bayesian inference. As there is no specific analytical
procedure that allows us to identify the appropriate loss function to be used, most of the works on point estimation and
point prediction assume the underlying loss function to be squared error which is symmetric in nature. However, in-
discriminate use of SELF is not appropriate particularly in these cases, where the losses are not symmetric. Thus in
order to make the statistical inferences more practical and applicable, we often needs to choose an asymmetric loss
function. A number of asymmetric loss functions have been shown to be functional, see Zellner (1986), Chandra (2001)
etc. In the present work, we consider symmetric as well as asymmetric loss functions for better comprehension of
Bayesian analysis.
a) The first is the common squared error loss function given by:
3. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Int. J. Stat. Math. 056
)5(ˆ,ˆ 2
1 cl
which is symmetric, and ˆ represent the true and estimated values of the parameter. This loss function is frequently
used because of its analytical tractability in Bayesian analysis.
b) The second is the Al-Bayyati’s loss function of the form
)6(,)(),( 2
22
Rcl c
c) The third is the precautionary loss function given by:
)7(
ˆ
ˆ
,ˆ
2
l
which is an asymmetric loss function, for details, see Norstrom (2012). This loss function is interesting in the sense that
a slight modification of squared error loss introduces asymmetry.
Maximum Likelihood Estimation
In this section we consider maximum likelihood estimators (MLE) of Lomax distribution. Let x1, x2,…, xn be a random
sample of size n from Lomax distribution, then the log likelihood function can be written as
n
i
x
nnL
1
1ln)1(lnln),(ln
As the parameter is assumed to be known, the ML estimator of is obtained by solving the equation
0
),(ln
L
01ln
1
n
i
xn
)8(
1ln
1
n
i
ML
x
n
Bayesian estimation of Lomax distribution under Jeffrey’s prior by using different loss function:
Consider n recorded values, ),...,,( 21 nxxxx having probability density function as
01),;(
)1(
x
x
xf
The likelihood function is given by
n
i
n
x
xL
1
)1(
1)/(
Thus, in our problem we consider the prior distribution of to be
)()( Ig
4. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Ahmad et al. 057
where k-vector is valued parameter and )(I is the Fisher’s information matrix of order .kk For the model (2) the
prior distribution is given by
1
)( g
The posterior distribution of is given by
)()/()/( gxLx
n
i
n
x
x
1
)1(
1
1)/(
n
i
n
n
x
x
1
1
1ln)1(exp)/(
n
i
n x
kx
1
1
1lnexp)/(
where k is independent of
and
d
x
k
n
i
n
0 1
11
1lnexp
n
n
i
x
n
k
1
1
1ln
n
x
k
n
n
i
1
1ln
Hence posterior distribution of is given by
n
i
n
n
n
i x
n
x
x
1
11
1lnexp
1ln
)/(
)9(exp)/( 1
t
n
t
x n
n
where
n
i
x
t
1
1ln
Estimator under squared error loss function
By using squared error loss function
2
1 )(),(
cl for some constant c1 the risk function is given by
),()( lER
dxl
0
)/(),(
5. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Int. J. Stat. Math. 058
dt
n
t
c n
n
exp)( 12
0
1
dtdtdt
n
tc nnn
n
exp2expexp
0
11
0
12
0
11
2
12
1 )1(
2
)2(
2
nnn
n
t
n
t
n
t
n
n
tc
t
nc
t
nnc
c
1
2
1
2
1
2)1(
Now solving 0
)(
R
, we obtain the Baye’s estimator as
0
2)1( 1
2
1
1
2
t
nc
t
nnc
c
0
2
2 1
1
t
nc
c
t
n
s
)10(
1ln
1
n
i
s
x
n
Estimation under Al-Bayyati’s Loss Function
Al-Bayyati, [5] introduced a new loss function given as
2
)(),( 2
c
l . Employ this loss function, we obtain the
Baye’s estimator under Jeffery prior information.
By using this loss function, we obtained the following risk function
dxR c
)/()()( 2
0
2
dt
n
t
R n
n
c
exp)()( 12
0
2
0
12
)exp()()( 2
dt
n
t
R cn
n
t
cn
t
cn
cn
nt
R c
)1(
2
)2(
)(
1
)( 2
2
2
2
2
2
6. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Ahmad et al. 059
Now solving 0
)(
R
, we obtain the Baye’s estimator as
0
)1(
2
)2(
)(
1 2
2
2
2
2
2
t
cn
t
cn
cn
ntc
0
)1(2
)(2
1 2
22
t
cn
cn
ntc
t
cn
A
2
)11(
1ln
1
2
n
i
A
x
cn
Estimation under Precautionary Loss Function:
For determining the Baye’s estimator of we will introduce asymmetric precautionary loss function given by
2
)(
),(l
By using this loss function the risk function is given by
0
1
2
exp
)(
)(
dt
n
t
R n
n
0
122
exp)()(
dt
n
t
R n
n
t
nc
t
nnc
c 1
2
1
1
2)1(
Now solving 0
)(
R
, we obtain the Baye’s estimator as
)12(
1ln
)1(
1
2
1
n
i
p
x
nn
Bayesian estimation of Lomax distribution under the extension of Jeffrey’s prior by using different loss
function
We consider the extended Jeffery prior is taken as
RcIg
c
,)()(
7. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Int. J. Stat. Math. 060
where
2
),;(log
)(
xf
nEI is the Fisher’s information matrix. For the model (2) the prior distribution of is
given by
c
g 2
1
)(
The posterior distribution of is given by
n
i
c
n
x
x
1
2
)1(
1
1)/(
n
i
n
cn
x
x
1
2
1ln)1(exp)/(
n
i
cn x
kx
1
2
1lnexp)/(
where k is independent of
and
d
x
k
n
i
cn
0 1
21
1lnexp
12
1
1
1ln
)12(
cn
n
i
x
cn
k
)12(
1ln
12
1
cn
x
k
cn
n
i
Hence posterior distribution of is given by
)13(exp
)12(
)/( 2
12
t
cn
t
x cn
cn
where
oftindependenis
x
t
n
i
1
1ln
Estimator under squared error loss function
By using squared error loss function
2
1 )(),(
cL for some constant c the risk function is given by
dt
cn
t
cR cn
cn
exp
)12(
)()( 2
12
2
0
1
n
i
cn
cn
n
i x
cn
x
x
1
2
12
1
1lnexp
)12(
1ln
)/(
8. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Ahmad et al. 061
123212
12
1 )12(
2
)32()12(
)12(
2
cncncn
cn
t
cn
t
cn
t
cn
cn
tc
t
cnc
t
cncnc
c
)12(2)12)(22( 1
2
12
1
Now solving 0
)(
R
, we obtain the Baye’s estimator as
)14(
1ln
1212
1
n
i
ss
x
cn
t
cn
Remark 1.1: Replacing c= 1/2 in (14), we get the same Bayes estimator as obtained in (10) corresponding to the
Jeffrey’s prior.
Estimation under Al-Bayyati’s Loss Function
By using the Al-Bayyati’s loss function the risk function is given by
dt
cn
t
R cn
cn
c
)exp(
)12(
)()( 2
12
0
22
0
22
12
)exp()(
)12(
)( 2
dt
cn
t
R ccn
cn
22
2
32
2
12
22
12
222
)22(
2
)32()12(
)12(
)( ccnccnccn
cn
t
ccn
t
ccn
t
ccn
cn
t
R
t
ccn
t
ccn
ccn
cntc
)22(
2
)32(
)12(
)12(
1 2
2
2
2
2
2
Now solving 0
)(
R
, we obtain the Baye’s estimator as
0
)22(
2
)32(
)12(
)12(
1 2
2
2
2
2
2
t
ccn
t
ccn
ccn
cntc
)15(
1ln
1212
1
22
n
i
AA
x
ccn
t
ccn
Remark 1.2: Replacing c= 1/2 in (15), we get the same Bayes estimator as obtained in (11) corresponding to the
Jeffrey’s prior.
Estimation under Precautionary loss function
By using precautionary loss function
2
)(
),(l the risk function is given by
9. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Int. J. Stat. Math. 062
dt
cn
t
R cn
cn
exp
)12(
)(
)( 2
12
0
2
t
cn
t
cncn
R
)12(2)12)(22(
)(
2
Now solving 0
)(
R
, we obtain the Baye’s estimator as
)16(
1ln
)12)(22(
1
2
1
n
i
p
x
cncn
Remark 1.3: Replacing c= 1/2 in (16), we get the same Bayes estimator as obtained in (12) corresponding to the
Jeffrey’s prior.
Simulation Study
In our simulation study, we chose a sample size of n=25, 50 and 100 to represent small, medium and large data set. The
shape parameter is estimated for Lomax distribution with Maximum Likelihood and Bayesian using Jeffrey’s & extension
of Jeffrey’s prior methods. For the shape parameter we have considered = 0.5 and 1.5. The values of Jeffrey’s
extension were c = 0.5 and 1.0. The value for the loss parameter c2 = 1.0 and 2.0. This was iterated 5000 times and
the shape parameter for each method was calculated. A simulation study was conducted R-software to examine and
compare the performance of the estimates for different sample sizes with different values for the Extension of Jeffreys’
prior and the loss functions. The results are presented in tables for different selections of the parameters and c
extension of Jeffrey’s prior.
Table 1. Mean Squared Error for )(
under Jeffery’s prior
n
ML
S A
c2=1
A
c2= -1
A
c2= 2.0
A
c2 = -2.0
p
25 0.5 1.0 0.0118 0.0113 0.0129 0.0106 0.0154 0.0108 0.0120
1.5 1.0 0.1298 0.1255 0.1492 0.1106 0.1815 0.1043 0.1362
0..5 2.0 0.0111 0.0107 0.0090 0.0131 0.0079 0.0161 0.0098
1.5 2.0 0.0872 0.0840 0.0777 0.0966 0.0780 0.1156 0.0801
50 0.5 0.5 0.0050 0.0049 0.0050 0.0049 0.0053 0.0052 0.0049
1.5 1.5 0.0811 0.0800 0.0918 0.0704 0.1059 0.0630 0.0856
0.5 0.5 0.0056 0.0055 0.0059 0.0052 0.0066 0.0052 0.0057
1.5 1.5 0.0680 0.0682 0.0591 0.0786 0.0514 0.0904 0.0635
100 0.5 0.5 0.0024 0.0024 0.0024 0.0024 0.0024 0.0025 0.0024
1.5 1.5 0.0752 0.0751 0.0691 0.0813 0.0634 0.0880 0.0721
0.5 0.5 0.0028 0.0028 0.0030 0.0027 0.0033 0.0026 0.0029
1.5 1.5 0.0242 0.0240 0.0225 0.0259 0.0214 0.0282 0.0232
ML= Maximum Likelihood, S=SELF, A= Al-Byatti’s Loss Function, P= Precautionary Loss Function
In Table 1, Bayes estimation with Al-Bayytai’s Loss function under Jeffrey’s prior provides the smallest values in
most cases especially when loss parameter C2 is -1, - 2.
10. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Ahmad et al. 063
Table 2. Mean Squared Error for )(
under extension of Jeffery’s prior
n C
ML
S A
c2=1
A
c2=-1
A
c2=2
A
c2=-2
p
25 0.5 1.0 0.5 0.0118 0.0113 0.0129 0.0106 0.0154 0.0108 0.0120
0.5 1.0 1.0 0.0143 0.0117 0.0133 0.0110 0.0160 0.0112 0.0124
1.5 1.0 0.5 0.1007 0.0979 0.0822 0.1192 0.0721 0.1461 0.0894
1.5 1.0 1.0 0.0872 0.0934 0.0808 0.1124 0.0745 0.1379 0.0863
0.5 2.0 0.5 0.0260 0.0102 0.0087 0.0124 0.0079 0.0152 0.0094
0.5 2.0 1.0 0.0158 0.0134 0.0157 0.0120 0.0191 0.0117 0.0144
1.5 2.0 0.5 0.1073 0.1045 0.0866 0.1281 0.0739 0.1568 0.0949
1.5 2.0 1.0 0.0977 0.0880 0.0900 0.0939 0.0994 0.1074 0.0881
50 0.5 1.0 0.5 0.0052 0.0050 0.0054 0.0050 0.0059 0.0051 0.0052
0.5 1.0 1.0 0.0059 0.0067 0.0058 0.0078 0.0051 0.0090 0.0063
1.5 1.0 0.5 0.2795 0.2781 0.3147 0.2443 0.0354 0.2137 0.2959
1.5 1.0 1.0 0.0972 0.1094 0.0960 0.1240 0.0833 0.1399 0.1026
0.5 2.0 0.5 0.0112 0.0112 0.0098 0.0127 0.0085 0.1445 0.0105
0.5 2.0 1.0 0.0077 0.0087 0.0075 0.0103 0.0065 0.0115 0.0081
1.5 2.0 0.5 0.1225 0.1212 0.1398 0.1051 0.1608 0.0914 0.1301
1.5 2.0 1.0 0.1525 0.1682 0.1514 0.1859 0.1356 0.2048 0.1597
100 0.5 1.0 0.5 0.0025 0.0025 0.0025 0.0025 0.0027 0.0025 0.0025
0.5 1.0 1.0 0.0024 0.0025 0.0023 0.0026 0.0023 0.0028 0.0024
1.5 1.0 0.5 0.0229 0.0226 0.0216 0.0240 0.0211 0.0258 0.0221
1.5 1.0 1.0 0.0516 0.0564 0.0513 0.0618 0.0466 0.0675 0.0538
0.5 2.0 0.5 0.0027 0.0026 0.0027 0.0025 0.0029 0.0025 0.0026
0.5 2.0 1.0 0.0025 0.0026 0.0025 0.0028 0.0023 0.0031 0.0025
1.5 2.0 0.5 0.0736 0.7377 0.0808 0.0664 0.0890 0.0601 0.0770
1.5 2.0 1.0 0.0225 0.0222 0.0221 0.0228 0.0223 0.0239 0.0221
ML= Maximum Likelihood, S=SELF, A= Al-Bayytai’s Loss Function, P= Precautionary Loss Function
In Table 2, Bayes estimation with Al-Bayytai’s Loss function under extension of Jeffrey’s prior provides the smallest
values in most cases especially when loss parameter C2 is -1,-2 whether the extension of Jeffrey’s prior is 0.5, 1.0.
Moreover, when the sample size increases from 25 to 100, the MSE decreases quite significantly.
Application
Here, we use a real data set to compare the estimates of the Lomax distribution. We consider an uncensored data set
corresponding an uncensored data set from consisting of 100 observations on breaking stress of carbon fibers (in Gba):
3.7, 2.74, 2.73, 2.5, 3.6, 3.11, 3.27,2.87, 1.47, 3.11,4.42, 2.41, 3.19, 3.22, 1.69, 3.28, 3.09, 1.87, 3.15, 4.9, 3.75, 2.43,
2.95, 2.97, 3.39, 2.96, 2.53,2.67, 2.93, 3.22, 3.39, 2.81, 4.2, 3.33, 2.55, 3.31, 3.31, 2.85, 2.56, 3.56, 3.15, 2.35, 2.55,
2.59,2.38, 2.81, 2.77, 2.17, 2.83, 1.92, 1.41, 3.68, 2.97, 1.36, 0.98, 2.76, 4.91, 3.68, 1.84, 1.59, 3.19,1.57, 0.81, 5.56,
1.73, 1.59, 2, 1.22, 1.12, 1.71, 2.17, 1.17, 5.08, 2.48, 1.18,3.51, 2.17, 1.69,1.25, 4.38, 1.84, 0.39, 3.68, 2.48, 0.85, 1.61,
2.79, 4.7, 2.03, 1.8, 1.57, 1.08, 2.03, 1.61, 2.12,1.89, 2.88, 2.82, 2.05, 3.65. These data are used here only for
illustrative purposes. The required numerical evaluations are carried out using the Package of R software.
We used the non-informative Jeffery’s priors for θ when = 1, 2, values of Jeffrey’s extension were c = 1.0 and when c
= 0.5 it gives same estimates as in case of Jeffery’s prior (Table 3). The value of loss parameters c=(1, -1, 2, -2) The
estimated results are given at Table 3 and 4.
11. Bayesian analysis of shape parameter of Lomax distribution using different loss functions
Int. J. Stat. Math. 064
Table 3: Estimates incase of Jefffery’s prior
ML
S A
c2=1
A
c2= -1
A
c2= 2.0
A
c2 = -2.0
p
1.0 0.0978 0.0977 0.1026 0.0929 0.1076 0.0882 0.1001
2.0 0.5471 0.5469 0.5650 0.5291 0.5834 0.5116 0.5560
Table 4. Estimates in case of extension of Jeffery’s prior
C
ML
S A
c2=1
A
c2=-1
A
c2=2
A
c2= -2
p
1.0 1.0 0.0978 0.0929 0.0977 0.0882 0.1026 0.0837 0.0953
2.0 1.0 0.5471 0.5290 0.5468 0.5115 0.5649 0.4943 0.5379
From these tables we conclude that Al-Bayytai’s loss is best among these as it gives the smallest values of estimates
especially when c2 = -1 , -2.
CONCLUSION
In this article, we have primarily studied the Bayes estimator of the parameter of the Lomax distribution under the
Jeffery’s and extended Jeffrey’s prior assuming three different loss functions. The extended Jeffrey’s prior gives the
opportunity of covering wide spectrum of priors to get Bayes estimates of the parameter - particular cases of which are
Jeffrey’s prior and Hartigan’s prior. We have also addressed the problem of Bayesian estimation for the Lomax
distribution, under symmetric loss functions and that of Maximum Likelihood Estimation. From the results, we observe
that in most cases, Bayesian Estimator under New Loss function (Al-Bayyati’s Loss function) has the smallest Mean
Squared Error values for both prior’s i.e, Jeffrey’s and an extension of Jeffrey’s prior information.
ACKNOWLEDGMENT
The authors would like to thank the referee for a very careful reading of the manuscript and making a number of nice
suggestions which improved the earlier version of the manuscript.
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